Fig 7. Average vs. Difference Scale Factors for Area-Preserving and Space-Filling/Area-Increasing Principles.

The functional dependence between the average scale factors (β, γ) and the difference scale factors (Δβ, Δγ) are graphed. For both cases of either the square-law (area-preserving) or the cube-law (space-filling and area-increasing) the average scale factors decrease from 1/2^1/2 and 1/2^1/3, respectively, and converge to 0.5 as the difference scale factors increase from 0 to 0.5.